Holographic lens with aberration correction

ABSTRACT

A technique for holographically constructing a lens made of stacked Fresnel zone plates on a thick emulsion photographic film which is capable of imaging a wide object field by joining the individual fields of each superimposed Fresnel zone plate to form an unaberrated composite image. The extent of the individual zone plate field is determined by the emulsion thickness and optical construction geometry and thereby allows restriction of this field to a size capable of unaberrated imaging.

UIIIIGG States Patent go fsm/ [72] Inventor Emmett N. Leith Plymouth.Mich. 121 1 Appl No. 730,447 [22] Filed May 20. I968 145] Patented June22, I97] [73] Assignee The Buttelle Development Corporation Columbus,Ohio [54] HOLOGRAPHIC LENS WITH ABERRATION CORRECTION 8 Claims, l0Drawing Figs. [52] US. Cl 350/15, 350/162 [51] Int. Cl G02b 27/22 [50]Field oISearch 350/35, 162

[56] References Cited OTHER REFERENCES Horman et al APPLIED OPTICS. Vol.6 No. 2, pp. 317 322(2/1967) Leith et al., .I. OPT. SOC. AM., Vol. 57No. 5, p. 699 (5/1967) Rosen. PROCEEDINGS OF THE IEEE. pp 1736- I73710/1967) Kock, PROCEEDINGS OF THE IEEE. pp 16l0- 1612 I 1/1967) Kock etal., PROCEEDINGS OF THE IEEE, pp. 1599- 1601(11/1967) Erdos. IBM TECH.DISC BULLETIN, Vol. 9, p. 291 (8/1966) Conger et al., 7 APPLIED OPTICS623 24, (4/1968) Primary Examiner-David Schonberg AssistantExaminer-Robert L. Sherman Attorney-Woodcock, Kurtz & MachiewiczABSTRACT: A technique for holographically constructing a lens made ofstacked Fresnel zone plates on a thick emulsion photographic film whichis capable of imaging a wide object field by joining the individualfields of each superimposed Fresnel zione plate to form an unaberratedcomposite image. The extent of the individual zone plate field isdetermined by the emulsion thickness and optical construction geometryand thereby allows restriction of this field to a size capable ofunaberrated imaging.

PATENTEU JUN22 I97:

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BACKGROUND OF THE INVENTION This invention is related generally tooptical imaging and more specifically to. imaging by a holographicallyconstructed Fresnel zone plate.

Traditional optical imaging by lenses involves bending light rays froman object by a refraction phenomenon into a focused image of the object.It has long been recognized that the wavefront image is not of goodfidelity because of lens aberrations which are generally classified intofive groups: coma, distortion, astigmatism, curvature of field, andspherical aberration. Such lens imperfections have been solved byspecially shaping lenses or by placing multiple lenses, each withdifferent refractory characteristics, in tandem so that each compensatesfor some imperfection in another. The need for aberration correction isespecially severe when an optical element is called upon to image alarge object field over a wide viewing angle.

More recently, Fresnel zone plates have been employed for opticalimaging by a diffraction phenomenon. A Fresnel zone plate is oftenpreferred over a lens, since a desired focal length may be obtainedeasily and inexpensively. As is well known, one technique to construct aFresnel zone plate is to interfere two coherent light beams at a finiteangle therebetween in a manner determined by the desired focal length.This interference pattern is recorded on a detector which is generallyphotographic film but may also be photochromic glass, F- centercrystals, or some other appropriate radiation detecting material. A zoneplate may be so constructed to be free of spherical aberrations betweencertain focal planes, but the remaining four aberrations exist. Onecompensation approach is to place several zone plates in tandem foraberration correction, much like the lens technique.

Therefore, it is a primary object of this invention to simplifyaberration correction in a Fresnel zone plate for improved imagingquality overa wide field of view.

It is another object of this invention to provide a simplified techniquefor improving image quality of large fields of view.

SUMMARY OF THE INVENTION These and additional objects are accomplishedby the method of constructing several zone plates in a singlethreedimensional detector media in a manner that each zone plate imagesonly a small distinct part of the object field that is within itsaberration-free range. A partitioned field zone plate holographic lensso constructed is then used as an optical element to fonn a compositeaberration-free image of the entire object field by joining together theimages of each individual zone plate. A partitioned field zone plate isformed by multiple exposure to off-axis coherent radiation beams.

The subject matter regarded as this invention is described in theappended claims, but the invention may be best understood by referenceto the following description taken in connection with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I illustrates one configurationfor making a Fresnel zone plate by holographic techniques.

FIG. 2 illustrates a method for holographically constructing a Fresnelzone plate with characteristics different from the plate constructedaccording to FIG. I.

FIG. 3 illustrates the imaging properties of a Fresnel zone plateconstructed according to the configuration of FIG. 1.

FIG. 4 illustrates the imaging characteristics of a Fresnel zone platewhich has been holographically constructed in a three-dimensionaldetector media.

FIG. 5 illustrates the light intensity diffraction efficiency of atypical three-dimensional Fresnel zone plate.

FIG. 6 illustrates one technique for constructing a partitioned fieldzone plate according to this invention.

FIG. 7 illustrates the use of a partitioned field zone plate constructedaccording to the configuration of FIG. 6.

FIG. 8 illustrates a technique for constructing a more generalpartitioned field zone plate according to this invention.

FIG. 9 illustrates a technique for making a partitioned field zone plateaccording to this invention by the techniques employed to construct aback beam hologram.

FIG. 10 shows a use of tandem partitioned field zone plates.

DESCRIPTION OF THE PREFERRED EMBODIMENTS I7 and a beam 19. The lightbeam I9 is reflected from a mirror 21 into a lens 23. A pinhole filter25 is placed at the focal point of the lens 23, assuming the beam 19 tobe substantially collimated. A resulting clean diverging light beam 27is then directed to a radiation detector 29 which is usually aphotographic film. This configuration illuminates the detector 29 in amanner as if a point light source were placed at position 31 a distanceR, from the center of the detector 29.

The light beam 17 is reflected from a mirror 33 into a lens 35. Apinhole filter 39 is placed at the focal plane of the lens 35 to presenta clean diverging beam 41 to a collimating lens 43 and a beam converginglens 45. The converging light beam 47 then strikes the detector 29 in amanner to appear to originate from a virtual point source at point 49 ata distance R, from the center of the detector 29.

In FIG. 2, a similar arrangement to that of FIG. I is shown, except thatthe converging beam 47 is replaced by a diverging beam 51 which appearsto come from a point light source 53 a distance -R, from the center ofthe detector 29. This configuration is illustrated to show theflexibility available in constructing a Fresnel zone plate and the usesof these con structed plates will be discussed hereinafler.

As a background to aid in the explanation of the principles of thepresent invention, the use of a Fresnel zone plate as constructed by theconfiguration of FIG. 1 will be examined in some detail. If the detector29 is a photographic film, this film is developed in a normal mannerafter exposureto the interference pattern of the diverging beam 27 andthe converging beam 47 to result in a diffraction grating transparencywhich is the desired Fresnel zone plate 29' of FIG. 3. If illuminatedpoint 0 is placed relative to zone plate 29' to be coincident with theapparent point light source 31 used in construction, the point 0 will beimaged by the zone plate to point i which is coincident with theapparent point virtual source 49 of the construction step of FIG. 1. Thefocal length of the zone plate 29 may be described by the fundamentallens formula,

1/f=' 1 which may be expressed as,

Fm. O/( H' If a second point 0 is located a distance R, from the zoneplate along a radial line angularly displaced 0, from the radial line R,to point 0, an images" of this point a distance R, will result which isrotated through an angle '9, from the radial distance R The location ofi" may be determined as follows, since the focal length of the zoneplate 29' has been calculated according to equation (2):

l/FI/R,+l/R: (3)

Furthermore, 0, is approximately equal to 0,. It can be seen then that aFresnel zone plate may be utilized as an ordinary lens and the basiclaws of optics apply.

It should be noted that in construction of the Fresnel zone plate 29'according to the configuration of FIG. I, the distance R, is the radiusof curvature of the light wave front which apparently emanates from apoint source 31. Since the radius of curvature of this wave front willnot be constant along the detector 29, a point 55 approximately in thecenter of the detector 29 is chosen for convenience to measure the lightbeam curvature. Similarly, the radius of curvature of the wave frontapparently emanating from the virtual point source 49 is also meuured atthis approximate center point for convenience throughout this analysis.

As the object point of FIG. 3 moves further away from point 0, the lensformula (4) will not hold exactly because of the aforementionedaberrations of the Fresnel zone plate 29'. However, within a certainlimited range these aberrations are not noticeable. Therefore, if alimited object area 57 around point 0 in FIG. 4 is to be imaged ontoarea 59 around point i, the image will be substantially unaberratedthroughout all points of the area imaged. The field of view may belimited to this unaberrated region by. constructing the Fresnel zoneplate 61 from a three-dimensional detector media. Anexample of such amedia is a photographic film with a thick emulsion. When such a film isexposed according to the configuration of FIG. 1,.the zone plate 61 willhave angular sensitivity and will image light rays striking it onlywithin a certain range of angles The use of a three-dimensional detectorin the construction of a Fresnel zone plate causes the zone plate toproduce an angular discrimination in the intensity of the imageproduced. That is, light rays whose incident angle differs from theincident angle 0, used in the construction of the zone plate will havean intensity significantly reduced from those rays whose angle is 0,.This angular deviation, A0,, is measured in the plane formed by thepoints 0,1, and the center 62 of the zone plate 61, i.e. the plane ofthe paper in FIG. 4. The image intensity of object points near theobject point 0, but not in the plane of the paper, will have a somewhatreduced intensity but the intensity discrimination will in general notbe as sharp as for rotations in the plane of the paper.

The variation of intensity with angle can be more clearly understoodwith reference to FIG. 5. The intensity of the diffracted wave 1' isshown as a function of the angle 0, which is the angle that areconstructing light beam coming from an object or light source. willmake with the zone plate 61. It is seen that there is not a sharpdropoff of light intensity with angular change and A0, has beenindicated rather arbitrarily between points where the intensity of thediffracted wave has substantially dropped off. This characteristic curvewill change .if any of the following variables change: 0,, in FIG. I,the angle that a zone plate constructing beam strikes photographic film;the angle 0,+ 8, in the construction configuration of FIG. I, which isthe angle between the two interfering beams used to expose thephotographic film to make the zone plate; thirdly, the thickness of thephotographic film emulsion. For more complete information as to thisparticular characteristic of thick emulsion photographic film, referencemay be had to an article Holographic Data Storage in Three-DimensionalMedia," by E. N. Leith et al., appearing in Applied Optics, Vol. 5, No.8, (Aug. I966) page 1303.

In order to construct a zone plate which will provide unaberratedimaging over a larger object volume than that represented by the area 57of FIG. 4, several zone plates may be constructedon a single thickemulsion photographic film. Each individual zone plate will then becapable of imaging an incremental object volume. The photographic filmmay be exposed in a manner so that during its use the images of theindividual object volumes are fused together to result in a compositeimage which is the sum of the images from each of the individual zoneplates. In FIG. 6, a technique for constructing such a multiple zoneplate is illustrated. A thick emulsion photographic film 63 is exposedto a light wave 65 which appears to come from a point source 0 adistance R, from the film center. The film 63 is also exposed to a lightwave 67 which appears to come from the virtual point source 1' adistance R, from the film center. The two wave fronts 65 and 67 theninterfere and this interference pattern is recorded on the photographicfilm 63.

This exposure will create a zone plate with a limited field of view A0,,according to the principles described with reference to FIG. 5. The film63 is rotated into position 63' through an angle A0, which is related tothis angular field of view and another exposure is made to theinterfering wave fronts 65 and 67. A third exposure may be made if film63' is rotated an additional amount to a position 63", and similarly afourth exposure can be made when rotated to position 63". It should benoted that the angles A0,, A0,, and A0, need not be equal. The resultingpartition field zone plate 63 will then be capable of imaging aspherical surface of radius R, with a center of curvature at the centerpoint 69 of the zone plate 63 onto another spherical surface of radiusR, with a center of curvature at the same point 69. If the object whichis desired to be imaged without aberrations is not a spherical surface,the distances R, and R, may be altered between exposures duringconstruction to conform to the surface to be imaged.

In FIG. 7, the imaging of such an object field 71 into an image field 73is illustrated. The points 01, O2, O3, and 04, as well as 41, i2, i3,and i4, all illustrate positions of the two apparent point sources ofcoherent light which are used to construct the partition field zoneplate 64 by four exposures. This FIG. clearly illustrates how an objectfield 7 I may be partitioned into four zones and each imagedindependently to form a composite image 73 of these four zones.

A more general method of constructing a partition field zone plate isdescribed with reference to FIG. 8. A detector 75 is first illuminatedby point source 01 a distance R from an approximate center of thedetector 75 and corresponding to a point of an object field which isdesired to be imaged. A virtual point source is located at a position ila distance R from an approximate center of the hologram 75 and locatedwhere an image surrounding the point M will be desired to be produced bythe finished lens. Once these two points are fixed, the focal length ofthe lens may be calculated according to equation (2).

In making a second exposure, the point light source is moved to aposition 02 a distance R,,, from the hologram 75 and rotated an angle 0,with respect to the hologram from the first exposure. The virtual lightsource must be placed along a line shown to have been rotated 0, fromthe R line of the first exposure and at a point 2 a distance R, which iscalculated according to equation (4), where f is the focal length asdetermined by the first exposure. Similarly, a third or any number ofsubsequent points may be used to make additional zone plates whichcorrespond to the various volumes of an object field of some irregularshape which is to be imaged.

The invention has so far been described wherein the two interferinglight beams strike the holographic detector at one side. However, it maybe an advantage in certain circum-' stances where the detector isphotographic film to illuminate the emulsion from opposite sides as isshown in FIG. 9, a known technique for constructing back beam holograms.A real point source 0 and a real point source 1' illuminate thephotographic film 77 from opposite sides thereof. The advantage to thisconfiguration over that of the light striking the film from the sameside is that the diffraction efficiency characteristics of the resultingfilm will be different, generally having sharper cutoffs, and may be anadvantage for certain applications.

It should also be noted that the above techniques could be modified forconstructing a lens capable of imaging an object illuminated with morethan one wavelength, and thus be useful in color imaging. To constructsuch a zone plate, it will be necessary to illuminate the detector witha plurality of wavelengths for each exposure hereinabove described. Themultiple wavelengths used to construct the hologram may be appliedsimultaneously or one at a time, according to techniques of colorholography.

The techniques of this invention may also be used for a variety ofdesired results by placing in tandem several distinct partition fieldzone plates for various effects. For example, as already mentioned inconnection with FIG. 4, the angular discrimination of the imageintensity is sharp for rotations in the plane of the paper, but not forother rotations, say into the plane of the paper. Sharp angulardiscrimination in this plane can also be obtained by use of anotherpartitioned zone plate placed in tandem with the first plate. As shownin FIG. 10, the light emerging from a first zone plate 91 serves as theincident light for a second zone plate 93. Sharp angular discriminationcan be achieved in the plane formed by points OB, and the plane can beoriented at some angle different from the corresponding plane ofdiffraction for the first zone plate 5".

Other uses of tandem holographic lenses include (I) using multipleplates to simulate a thicker element than can be achieved with a singleplate, (2) orienting the sound plate so that the final light beamemerging from the pair will be in the same direction as the incidentbeam, and (3) use of a second plate to compensate for the chromaticdispersion that would be present from the use of a single element.

It shall be understood that the invention is not limited to the specificarrangements shown, and that changes and modifications may be madewithin the scope of the appended claims.

What I claim is: l. A method ofimaging an object field, comprising thesteps of:

constructing a plurality of Fresnel zone plates, each of said zoneplates being capable of imaging with substantial exclusivity a singleincremental volume of said object field different from the incrementalvolumes imaged by any others of the plurality of zone plates, the totalof said incremental object field volumes being that portion of theobject field to be imaged, whereby each of said volumes may be madesmall enough to be imaged by its associated Fresnel zone plate withoutsignificant aberration,

illuminating said object field with electromagnetic radiation, and

positioning said plurality of Fresnel zone plates relative to the objectfield to image their associated object field incremental volumes in amanner to form a composite image of the object field.

2. A method of constructing a holographic lens capable of imaging a wideobject field with a low level of aberration, comprising the steps of:

exposing a threedimensional photosensitive media simultaneously to afirst wave front of coherent light having a first center of curvaturelocated relative to said photosensitive media and a second wave front ofcoherent light having a second center of curvature located relative tosaid photosensitive media, said first and second wave fronts beingmutually coherent, thereby forming a first zone plate, and

making at least a second exposure of said photosensitive mediasimultaneously to mutually coherent third and fourth wave fronts oflight having third and fourth centers of curvature located relative tosaid photosensitive media, respectively, thereby forming a second zoneplate superimposed over the first zone plate,

the positions of said first and third centers of curvature being spaced8 sufficient distance from each other so that a point of said objectfield coincident with said first center of curvature is imaged only bythe first zone plate and a point of said object field coincident withsaid third center of curvature is imaged only by the second zone plate.

3. A method of constructing a holographic lens according to claim 2wherein a mathematical product of the distances from the photosensitivemedia to said first and second centers of curvature divided by a sum ofthese distances is equal to the same quantity as a product of thedistances from the photosensitive media to said third and fourth centersof curvature divided by a sum of these distances, said quantity beingthe focal length of said holographic lens.

4. A method of imaging a wide object field with a low aberration levelby using a holographic lens constructed according to the method of claim4 and further including the step of placing the lens relative to theilluminated object field to produce an image thereof.

5. A method of imaging a wide object field with a low aberration levelby using a holographic lens constructed according to the method of claim2 and further including the step of placing the lens with said first andthird centers of curvature located within said object field, therebyforming images at said second and fourth centers of curvature of thoseportions of said object field coincident with the holographic lens firstand third centers of curvature, respectively.

6. A method of imaging a wide object field with a low aberration levelby using a holographic lens, comprising the steps of:

intersecting two beams of mutually coherent electromagnetic radiationwithout pictorial information at a predetermined finite angletherebetween,

placing a three-dimensional detector media in said beams,

changing the relative rotational positions between said detector andsaid beams an incremental amount between said detector and said beams anincremental amount between successive exposures to said radiation,thereby to record on said detector a plurality of interference patternsbetween said beams in the form of a holographic lens, and

placing the lens relative to the object field to produce an imagethereof.

7. A method of imaging an object field, comprising the steps of:

constructing a plurality of Fresnel zone plates on a common area of athick photosensitive system by sequentially exposing said system to theintersection of a pair of mutually coherent electromagnetic radiationbeams having particular angles with respect to said system andparticular wave front curvatures of said beams for each exposure,thereby to construct an individual zone plate as a result of eachexposure,

said angles of intersection and said wave front curvatures being relatedbetween exposures for a given thickness of said photosensitive system sothat each of said zone plates is capable of imaging with substantialexclusivity a single incremental volume of said object field differentfrom the incremental volumes imaged by any others of the plurality ofzone plates, whereby each of said volumes may be made small enough to beimaged by its associated zone plate without significant aberration,illuminating said object field with electromagnetic radiation,and

positioning said photosensitive system relative to the object field sothat each zone plate constructed on said system images its associatedincremental volume of the object field to form a composite image of theobject.

8. A method of constructing a holographic lens according to claim 2wherein said first and second wave fronts are of the same radiationwavelength as said third and fourth wave fronts.

"M050 UN ITI'ID S'IA'II'IS IATICN'I OFFICE CERTIFICATE OF CORRECTIONPatent No. 3 1 D d June 22, 1971 Inventor) Emmett N. Leith It iscertified that error appears in the above-identified patent and thatsaid Letters Patent are hereby corrected as shown below:

Page 1, column 2 the firm name should be changed from Woodcock, Kurtz &Machiewicz to Woodcock, Washburn, Kurtz and Mackiewicz-.

Column 2, line 53, correct 29 to 29'-.

line 54, change the equation "l/f l/R l2/3 R to l/f l/R l/R line 56,change the equation "f (R R )/(R R) to f R R R R line 67, at the end ofthe equation after the hyphen the letter -f should be inserted.

Column 5, line 13, change the word "sound" to second.

Claim 4, line 8, change the number "4" to 2-.

Signed and sealed this 21 at day of December 1 971 (s EAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GO'PISCHALK Attesting Officer ActingCommissioner of Patents

1. A method of imaging an object field, comprising the steps of:constructing a plurality of Fresnel zone plates, each of said zoneplates being capable of imaging with substantial exclusivity a singleincremental volume of said object field different from the incrementalvolumes imaged by any others of the plurality of zone plates, the totalof said incremental object field volumes being that portion of theobject field to be imaged, whereby each of said volumes may be madesmall enough to be imaged by its associated Fresnel zone plate withoutsignificant aberration, illuminating said object field withelectromagnetic radiation, and positioning said plurality of Fresnelzone plates relative to the object field to image their associatedobject field incremental volumes in a manner to form a composite imageof the object field.
 2. A method of constructing a holographic lenscapable of imaging a wide object field with a low level of aberration,comprising the steps of: exposing a three-dimensional photosensitivemedia simultaneously to a first wave front of coherent light having afirst center of curvature located relative to said photosensitive mediaand a second wave front of coherent light having a second center ofcurvature located relative to said photosensitive media, said first andsecond wave fronts being mutually coherent, thereby forming a first zoneplate, and making at least a second exposure of said photosensitivemedia simultaneously to mutually coherent third and fourth wave frontsof light having third and fourth centers of curvature located relativeto said photosensitive media, respectively, thereby forming a secondzone plate superimposed over the first zone plate, the positions of saidfirst and third centers of curvature being spaced a sufficient distancefrom each other so that a point of said object field coincident withsaid first center of curvature is imaged only by the first zone plateand a point of said object field coincident with said third center ofcurvature is imaged only by the second zone plate.
 3. A method ofconstructing a holographic lens according to claim 2 wherein amathematical product of the distances from the photosensitive media tosaid first and second centers of curvature divided by a sum of thesedistances is equal to the same quantity as a product of the distancesfrom the photosensitive media to said third and fourth centers ofcurvature divided by a sum of these distances, said quantity being thefocal length of said holographic lens.
 4. A method of imaging a wideobject field with a low aberration level by using a holographic lensconstructed according to the method of claim 4 and further including thestep of placing the lens relative to the illuminated object field toproduce an image thereof.
 5. A method of imaging a wide object fieldwith a low aberration level by using a holographic lens constructedaccording to the method of claim 2 and further including the step ofplacing the lens with said first and third centers of curvature locatedwithin said object field, thereby forming images at said second andfourth centers of curvature of those portions of said object fieldcoincident with the holographic lens'' first and third centers ofcurvature, respectively.
 6. A method of imaging a wide object field witha low aberration level by using a holographic lens, comprising the stepsof: intersecting two beams of mutually coherent electromagneticradiation without pictorial information at a predetermined finite angletherebetween, placing a three-dimensional detector media in said beams,changing the relative rotational positions between said detector andsaid beams an incremental amount between said detector and said bEams anincremental amount between successive exposures to said radiation,thereby to record on said detector a plurality of interference patternsbetween said beams in the form of a holographic lens, and placing thelens relative to the object field to produce an image thereof.
 7. Amethod of imaging an object field, comprising the steps of: constructinga plurality of Fresnel zone plates on a common area of a thickphotosensitive system by sequentially exposing said system to theintersection of a pair of mutually coherent electromagnetic radiationbeams having particular angles with respect to said system andparticular wave front curvatures of said beams for each exposure,thereby to construct an individual zone plate as a result of eachexposure, said angles of intersection and said wave front curvaturesbeing related between exposures for a given thickness of saidphotosensitive system so that each of said zone plates is capable ofimaging with substantial exclusivity a single incremental volume of saidobject field different from the incremental volumes imaged by any othersof the plurality of zone plates, whereby each of said volumes may bemade small enough to be imaged by its associated zone plate withoutsignificant aberration, illuminating said object field withelectromagnetic radiation, and positioning said photosensitive systemrelative to the object field so that each zone plate constructed on saidsystem images its associated incremental volume of the object field toform a composite image of the object.
 8. A method of constructing aholographic lens according to claim 2 wherein said first and second wavefronts are of the same radiation wavelength as said third and fourthwave fronts.